Difference between revisions of "2006 AMC 12A Problems"
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== Problem 1 == | == Problem 1 == | ||
| − | Sandwiches at Joe's Fast Food cost $3 each and sodas cost $2 each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? | + | Sandwiches at Joe's Fast Food cost <math>$3</math> each and sodas cost <math>$2</math> each. How many dollars will it cost to purchase <math>5</math> sandwiches and <math>8</math> sodas? |
[[2006 AMC 12A Problem 1|Solution]] | [[2006 AMC 12A Problem 1|Solution]] | ||
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== Problem 3 == | == Problem 3 == | ||
| − | The ratio of Mary's age to Alice's age is 3:5. Alice is 30 years old. How old is Mary? | + | The ratio of Mary's age to Alice's age is <math>3:5</math>. Alice is <math>30</math> years old. How old is Mary? |
[[2006 AMC 12A Problem 3|Solution]] | [[2006 AMC 12A Problem 3|Solution]] | ||
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== Problem 5 == | == Problem 5 == | ||
| − | Doug and Dave shared a pizza with 8 equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was $8, and there was an additional cost of $2 for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each paid for what he had eaten. How many more dollars did Dave pay than Doug? | + | Doug and Dave shared a pizza with <math>8</math> equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was <math>$8</math>, and there was an additional cost of <math>$2</math> for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each paid for what he had eaten. How many more dollars did Dave pay than Doug? |
[[2006 AMC 12A Problem 5|Solution]] | [[2006 AMC 12A Problem 5|Solution]] | ||
== Problem 6 == | == Problem 6 == | ||
| + | |||
| + | ''(Missing Diagram)'' | ||
| + | |||
| + | The <math>8\times 18</math> rectangle <math>ABCD</math> is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is <math>y</math>? | ||
[[2006 AMC 12A Problem 6|Solution]] | [[2006 AMC 12A Problem 6|Solution]] | ||
== Problem 7 == | == Problem 7 == | ||
| + | |||
| + | Mary is <math>20%</math> older than Sally, and Sally is <math>40%</math> younger than Danielle. The sum of their ages is <math>23.2</math> years. How old will Mary be on her next birthday? | ||
[[2006 AMC 12A Problem 7|Solution]] | [[2006 AMC 12A Problem 7|Solution]] | ||
== Problem 8 == | == Problem 8 == | ||
| + | |||
| + | How many sets of two or more consecutive positive integers have a sum of <math>15</math>? | ||
[[2006 AMC 12A Problem 8|Solution]] | [[2006 AMC 12A Problem 8|Solution]] | ||
== Problem 9 == | == Problem 9 == | ||
| + | |||
| + | Oscar buys <math>13</math> pencils and <math>3</math> erasers for <math>$1.00</math>. A pencil costs more than an eraser, and both items cost a whole number of cents. What is the total cost, in cents, of one pencil and one eraser? | ||
[[2006 AMC 12A Problem 9|Solution]] | [[2006 AMC 12A Problem 9|Solution]] | ||
== Problem 10 == | == Problem 10 == | ||
| + | |||
| + | For how many real values of <math>x</math> is <math>\sqrt{120-\sqrt{x}}</math> an integer? | ||
[[2006 AMC 12A Problem 10|Solution]] | [[2006 AMC 12A Problem 10|Solution]] | ||
Revision as of 17:28, 30 June 2006
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Sandwiches at Joe's Fast Food cost 
each and sodas cost 
each. How many dollars will it cost to purchase 
sandwiches and 
sodas?
Problem 2
Define 
. What is 
?
Problem 3
The ratio of Mary's age to Alice's age is 
. Alice is 
years old. How old is Mary?
Problem 4
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?
Problem 5
Doug and Dave shared a pizza with equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was , and there was an additional cost of for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each paid for what he had eaten. How many more dollars did Dave pay than Doug?
Problem 6
(Missing Diagram)
The 
rectangle 
is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is 
?
Problem 7
Mary is $20%$ (Error compiling LaTeX. Unknown error_msg) older than Sally, and Sally is $40%$ (Error compiling LaTeX. Unknown error_msg) younger than Danielle. The sum of their ages is 
years. How old will Mary be on her next birthday?
Problem 8
How many sets of two or more consecutive positive integers have a sum of 
?
Problem 9
Oscar buys 
pencils and erasers for 
. A pencil costs more than an eraser, and both items cost a whole number of cents. What is the total cost, in cents, of one pencil and one eraser?
Problem 10
For how many real values of 
is 
an integer?
